Green’s Dictionary of Slang

off like a... phr.

[SE off, away + pun on off, stale]

In phrases

off like a bride’s nightie (also off like a prom dress, up and down like a bride’s nightie)

[1950s+] (Aus./US campus) leaving or acting extremely fast, very speedily.

off like a bucket of prawns in the (hot) sun [pun on SE off, stale]

[1990s+] (Aus.) leaving very quickly.

off like a robber’s dog

[1980s+] (Aus.) leaving very quickly.